Currently the Laser Interferometric Gravitational-wave Observatory (LIGO) is undergoing upgrades from Initial LIGO to become Advanced LIGO. Amongst these upgrades is the addition of a signal recycling mirror at the output port of the interferometer; upgrades of the mirror suspensions to quadruple pendulums; the implementation of less invasive and hence weaker test mass actuators; and the change of readout scheme from a heterodyne based RF readout to a homodyne based DC readout. The DC readout scheme requires the installation of an Output Mode Cleaner (OMC), to stop `junk light' generated in the interferometer from making its way to the DC photodetector where it can limit the sensitivity of the gravitational wave detector. The steering of the interferometer beam into the OMC will be handled by Tip Tilt mirrors designed at the Australian National University. The first core piece of work presented in this thesis was the characterisation of a prototype Tip Tilt mirror, which involved measuring the various eigenmodes of the mirror
